Numerical studies on Kerr frequency comb generation with vertically-coupled whispering-gallery-mode (WGM) Si3N4 resonators are presented. These resonators include a frequency-dependent access coupler and are characterized by a free spectral range (FSR) of 220 GHz. We present numerical simulations based on the Ikeda map that allows implementation of complex-valued frequency-dependent and non-reciprocal access coupler transfer matrix in the simulation of Kerr comb in the cavities modelled by Arlotti et al. We use a Runge-Kutta 4 Interaction picture (RK4IP) method with adaptive step-size control as developed by Balac et al. to circumvent the numerical burden added by this modelling approach and successfully simulate Kerr comb generation using an approach that accurately models any optical cavity that can be considered as spatially one-dimensional regardless of its quality factor, finesse or dispersive properties which comes in useful in this study when access coupling properties degrade the resonator quality factor.
Over the last two decades, integrated whispering-gallery-mode resonators have been increasingly used as the basic building blocks for selective filters, high-sensitivity sensors, and as nonlinear converters. In the latter two cases, optimum performance is achieved when the intra-cavity power or the resonance feature contrast are maximum. For devices with transversely singlemode resonator and access waveguides, the above-mentioned conditions are obtained when the system is critically coupled i.e. when the coupler power transfer rate corresponds to the single-pass intra-cavity loss. Designing coupled resonators for which critical-coupling is maintained over a large spectral range is therefore attractive to facilitate sensing or nonlinear frequency conversion.
In this paper, we theoretically show, using a generic model based on the universal description of the device spectral characteristics and a coupled-mode theory treatment of the coupling section, that access-waveguide-coupled resonators can exhibit a wideband critical-coupling bandwidth when their constitutive resonator and access waveguides are different i.e. when they are phase-mismatched. To illustrate this, we have calculated the spectral response of Si3N4/SiO2 racetrack resonators and have found that, when the coupler beat-length becomes achromatic, the device critical-coupling bandwidth is expanded by more one order of magnitude compared to their phase-matched counterpart.
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